Approximate distributed top-k queries

Patt-Shamir, Boaz; Shafrir, Allon

doi:10.1007/s00446-008-0055-3

Cited by 7 publications

(7 citation statements)

References 29 publications

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“…We can show that to achieve the success guarantee, z should be at least Ω(k). This result is perhaps folklore; proofs to more general versions of this problem can be found in [4] (Chapter 4), and also [22,27]. We include a simpler proof in the appendix for completeness.…”

Section: Lemma 22 Immediately Implies the Following Theoremmentioning

confidence: 85%

Randomized Algorithms for Tracking Distributed Count, Frequencies, and Ranks

Huang

Zhang

2018

Algorithmica

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We show that randomization can lead to significant improvements for a few fundamental problems in distributed tracking. Our basis is the count-tracking problem, where there are k players, each holding a counter n i that gets incremented over time, and the goal is to track an ε-approximation of their sum n = i n i continuously at all times, using minimum communication. While the deterministic communication complexity of the problem is Θ(k/ε · log N ), where N is the final value of n when the tracking finishes, we show that with randomization, the communication cost can be reduced to Θ( √ k/ε · log N ). Our algorithm is simple and uses only O(1) space at each player, while the lower bound holds even assuming each player has infinite computing power. Then, we extend our techniques to two related distributed tracking problems: frequency-tracking and rank-tracking, and obtain similar improvements over previous deterministic algorithms. Both problems are of central importance in large data monitoring and analysis, and have been extensively studied in the literature. 1 We sometimes omit "(t)" when the context is clear. 2 A more careful analysis leads to a slightly better bound of O(k/ε · log(εN/k)), but we will assume that N is sufficiently large, compared to k and 1/ε, to simplify the bounds.

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Section: Lemma 22 Immediately Implies the Following Theoremmentioning

confidence: 85%

Randomized Algorithms for Tracking Distributed Count, Frequencies, and Ranks

Huang

Zhang

2018

Algorithmica

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show abstract

“…We can show that to achieve the success guarantee, z should be at least Ω(k). This result is perhaps folklore; proofs to more general versions of this problem can be found in [4] (Chapter 4), and also [21,25]. We include a simpler proof in the appendix for completeness.…”

Section: Lemma 22 Immediately Implies the Following Theoremmentioning

confidence: 82%

Randomized algorithms for tracking distributed count, frequencies, and ranks

Huang

Zhang

2012

Proceedings of the 31st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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We show that randomization can lead to significant improvements for a few fundamental problems in distributed tracking. Our basis is the count-tracking problem, where there are k players, each holding a counter ni that gets incremented over time, and the goal is to track an ε-approximation of their sum n = i ni continuously at all times, using minimum communication. While the deterministic communication complexity of the problem is Θ(k/ε · log N ), where N is the final value of n when the tracking finishes, we show that with randomization, the communication cost can be reduced to Θ( √ k/ε · log N ). Our algorithm is simple and uses only O(1) space at each player, while the lower bound holds even assuming each player has infinite computing power. Then, we extend our techniques to two related distributed tracking problems: frequency-tracking and rank-tracking, and obtain similar improvements over previous deterministic algorithms. Both problems are of central importance in large data monitoring and analysis, and have been extensively studied in the literature.

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“…This server-site model has been widely studied in the databases and distributed computing communities. Work includes computing top-k [9,32,35] and heavy hitters [45,22]. Another closely related model is the distributed monitoring model, in which we also have one server and k sites.…”

Section: Motivation Previous Work and Related Modelsmentioning

confidence: 99%

Lower Bounds for Number-in-Hand Multiparty Communication Complexity, Made Easy

Phillips¹,

Verbin²,

Zhang³

2016

SIAM J. Comput.

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In this paper we prove lower bounds on randomized multiparty communication complexity, both in the blackboard model (where each message is written on a blackboard for all players to see) and (mainly) in the message-passing model, where messages are sent player-to-player. We introduce a new technique for proving such bounds, called symmetrization, which is natural, intuitive, and often easy to use.For example, for the problem where each of k players gets a bit-vector of length n, and the goal is to compute the coordinate-wise XOR of these vectors, we prove a tight lower bounds of Ω(nk) in the blackboard model. For the same problem with AND instead of XOR, we prove a lower bounds of roughly Ω(nk) in the message-passing model (assuming k ≤ n/3200) and Ω(n log k) in the blackboard model. We also prove lower bounds for bit-wise majority, for a graph-connectivity problem, and for other problems; the technique seems applicable to a wide range of other problems as well. All of our lower bounds allow randomized communication protocols with two-sided error.We also use the symmetrization technique to prove several direct-sum-like results for multiparty communication.

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Approximate distributed top-k queries

Cited by 7 publications

References 29 publications

Randomized Algorithms for Tracking Distributed Count, Frequencies, and Ranks

Randomized Algorithms for Tracking Distributed Count, Frequencies, and Ranks

Randomized algorithms for tracking distributed count, frequencies, and ranks

Lower Bounds for Number-in-Hand Multiparty Communication Complexity, Made Easy

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